Precalculus / College Algebra, 3rd Edition
The first half of a precalculus series, covering college algebra. This text takes a "functions first" approach, introducing the idea of a function early. Then as each class of functions is introduced, equations, inequalities, and applications involving functions in that class are discussed. The material is presented at a level to prepare the student for calculus an well as give them relevant mathematics which can be used in other classes as well. Graphing utilities are used sparingly to enhance the mathematics. The exercise sets were intentionally kept smaller to cover all the necessary skills and get the students thinking more deeply about the mathematics involved.
License: Creative Commons Attribution Sharealike Noncommercial. This license is very open. It allows reuse, remixing, and distribution, but prohibits commercial use and requires any remixes use the same license as the original. This limits where the content can be remixed into, but on the other hand ensures that no-one can remix the content then put the remix under a more restrictive license. The non-commercial clause can make getting printed copies of remixes challenging depending upon how strictly the authors interpret the clause.
Formats:
- PDF. A Portable Document Format (PDF) file is can be opened using the free Acrobat Reader. It is not an editable format.
- TeX. A TeX file use the TeX or LaTeX typesetting engine. TeX software is available free for most platforms. It is an editable format
Openness Rating (0-4): 3
Openness Comments: Besides the non-commercial restriction, the use of MetaPost with TeX makes compiling the text after changes a non-trivial task. The authors have tried to help with this by posting how-to videos.
- Chapter 1: Relations and Functions
- 1.1 The Cartesian Coordinate Plane
- 1.2 Relations
- 1.3 Graphs of Equations
- 1.4 Introduction to Functions
- 1.5 Function Notation
- 1.6 Function Arithmetic
- 1.7 Graphs of Functions
- 1.8 Transformations
- Chapter 2: Linear and Quadratic Functions
- 2.1 Linear Functions
- 2.2 Absolute Value Functions
- 2.3 Quadratic Functions
- 2.4 Inequalities
- 2.5 Regression
- Chapter 3: Polynomial Functions
- 3.1 Graphs of Polynomials
- 3.2 The Factor Theorem and The Remainder Theorem
- 3.3 Real Zeros of Polynomials
- 3.4 Complex Zeros and the Fundamental Theorem of Algebra
- Chapter 4: Rational Functions
- 4.1 Introduction to Rational Functions
- 4.2 Graphs of Rational Functions
- 4.3 Rational Inequalities and Applications
- Chapter 5: Further Topics in Functions
- 5.1 Function Composition
- 5.2 Inverse Functions
- 5.3 Other Algebraic Functions
- Chapter 6: Exponential and Logarithmic Functions
- 6.1 Introduction to Exponential and Logarithmic Functions
- 6.2 Properties of Logarithms
- 6.3 Exponential Equations and Inequalities
- 6.4 Logarithmic Equations and Inequalities
- 6.5 Applications of Exponential and Logarithmic Functions
- Chapter 7: Hooked on Conics
- 7.1 Introduction to Conics
- 7.2 Circles
- 7.3 Parabolas
- 7.4 Ellipses
- 7.5 Hyperbolas
- Chapter 8: Systems of Equations and Matrices
- 8.1 Systems of Linear Equations: Gaussian Elimination
- 8.2 Systems of Linear Equations: Augmented Matrices
- 8.3 Matrix Arithmetic
- 8.4 Systems of Linear Equations: Matrix Inverses
- 8.5 Determinants and Cramer's Rule
- 8.6 Partial Fraction Decomposition
- 8.7 Systems of Non-Linear Equations and Inequalities
- Chapter 9: Sequences and the Binomial Theorem
- 9.1 Sequences
- 9.2 Summation Notation
- 9.3 Mathematical Induction
- 9.4 The Binomial Theorem
Supplements:
- MyOpenMath / Lumen OHM online homework. MyOpenMath is a free online homework system, built on the open source IMathAS assessment platform.
It provides randomized, algorithmically generated homework with automated grading of numerical and algebraic answers, similar to WebAssign and MyMathLab.
It also provides a course management system with gradebook, file posting, discussion forums, etc.
Assessment sets have been created for this textbook, which may be available for self-study by students, or can copied as a starter course shell by faculty.
MyOpenMath use is free with community support through forums. For Washington State faculty, the WAMAP.org site also mirrors this content.
Lumen OHM is a commercial alternative to MyOpenMath that provides support for faculty and large scale adoption and administration, service level agreements, and additional curated course bundles. - WebAssign online homework. WebAssign is a commercial online homework system. It provides randomized homework custom-built to align with textbooks. Question sets have been created for this textbook which can be built into assessment sets by faculty. They provide support.
- Videos. See the comments below for details.
Notes:
Powerpoint slides are available on the book website, along with checkpoint quizzes and video solutions to the quizzes.
The MyOpenMath starter course includes overview videos and online homework